Few group cross section representation based on sparse grid methods
This thesis addresses the problem of representing few group, homogenised neutron cross sections as a function of state parameters (e.g. burn-up, fuel and moderator temperature, etc.) that describe the conditions in the reactor. The problem is multi-dimensional and the cross section samples, required for building the representation, are the result of expensive transport calculations. At the same time, practical applications require high accuracy. The representation method must therefore be efficient in terms of the number of samples needed for constructing the representation, storage requirements and cross section reconstruction time. Sparse grid methods are proposed for constructing such an efficient representation. Approximation through quasi-regression as well as polynomial interpolation, both based on sparse grids, were investigated. These methods have built-in error estimation capabilities and methods for optimising the representation, and scale well with the number of state parameters. An anisotropic sparse grid integrator based on Clenshaw-Curtis quadrature was implemented, verified and coupled to a pre-existing cross section representation system. Some ways to improve the integrator’s performance were also explored. The sparse grid methods were used to construct cross section representations for various Light Water Reactor fuel assemblies. These reactors have different operating conditions, enrichments and state parameters and therefore pose different challenges to a representation method. Additionally, an example where the cross sections have a different group structure, and were calculated using a different transport code, was used to test the representation method. The built-in error measures were tested on independent, uniformly distributed, quasi-random sample points. In all the cases studied, interpolation proved to be more accurate than approximation for the same number of samples. The primary source of error was found to be the Xenon transient at the beginning of an element’s life (BOL). To address this, the domain was split along the burn-up dimension into “start-up” and “operating” representations. As an alternative, the Xenon concentration was set to its equilibrium value for the whole burn-up range. The representations were also improved by applying anisotropic sampling. It was concluded that interpolation on a sparse grid shows promise as a method for building a cross section representation of sufficient accuracy to be used for practical reactor calculations with a reasonable number of samples.
- Engineering